Our approach is related to and partially relies on work on modal intervals and mean-value extensions, which applications include the computation of under-approximations of function images [1]}, [2]}. It is also related to over-approximations of nonlinear functions and dynamical systems, on which we rely to compute under-approximations. Many methods for over-approximating reachable sets for non-linear systems have been developed, among which Taylor methods [3]} or polytopes-based methods [4]}, [5]}.
